Problem: How many ways are there to put 5 balls in 3 boxes if the balls are not distinguishable and neither are the boxes?
The ways to arrange indistinguishable balls into indistinguishable boxes only depends on the number of balls in the boxes.  The ways to do this are $(5,0,0)$, $(4,1,0)$, $(3,2,0)$, $(3,1,1)$, $(2,2,1)$.  There are $\boxed{5}$ ways.